# topcomRegularFineTriangulation(Matrix) -- compute a regular triangulation using all of the given points

## Description

This function returns a regular fine triangulation of the point set $A$ (that is, a list of lists of indices in the range $0, \ldots, n-1$, where $A$ is $d \times n$, and has full rank.

Recall: a fine triangulation is one which uses all of the points, and a regular triangulation is one which is induced as the lower faces of a lift of the points to one dimension higher.

Here we find a regular fine triangulation of the cyclic polytope with 7 vertices in 3-space.

 i1 : A = matrix {{0, 1, 2, 3, 4, 5, 6}, {0, 1, 4, 9, 16, 25, 36}, {0, 1, 8, 27, 64, 125, 216}} o1 = | 0 1 2 3 4 5 6 | | 0 1 4 9 16 25 36 | | 0 1 8 27 64 125 216 | 3 7 o1 : Matrix ZZ <--- ZZ i2 : tri = topcomRegularFineTriangulation A o2 = {{0, 1, 2, 3}, {1, 2, 3, 4}, {0, 1, 3, 4}, {2, 3, 4, 5}, {1, 2, 4, 5}, ------------------------------------------------------------------------ {0, 1, 4, 5}, {3, 4, 5, 6}, {2, 3, 5, 6}, {1, 2, 5, 6}, {0, 1, 5, 6}} o2 : List i3 : assert topcomIsTriangulation(A, tri) i4 : assert topcomIsRegularTriangulation(A, tri) i5 : topcomRegularTriangulationWeights(A, tri) 5 5 1 o5 = {-, -, -, 0, 0, 0, 0} 2 6 6 o5 : List